To prove tensoriality, we will use the method of [1]} and [2]} to show that we can break correlations over expanding collections of tuples arising in the \(s\) -wide replacement product of the form
\(\operatornamewithlimits{\mathbb {E}}_{\begin{array}{c}ww^{\prime } \in W[k_1,k_3] \\ w \in W[k_1,k_2], w^{\prime } \in W[k_2+1,k_3]\end{array}}{\left\Vert {\mathbf {Z}_{ww^{\prime }}} - {\mathbf {Z}_w} {\mathbf {Z}_{w^{\prime }}} \right\Vert _1}\) 
